Liouville Type Results and Regularity of the Extremal Solutions of Biharmonic Equation with Negative Exponents
نویسندگان
چکیده
We first obtain Liouville type results for stable entire solutions of the biharmonic equation −∆2u = u−p in R for p > 1 and 3 ≤ N ≤ 12. Then we consider the Navier boundary value problem for the corresponding equation and improve the known results on the regularity of the extremal solution for 3 ≤ N ≤ 12. As a consequence, in the case of p = 2, we show that the extremal solution u∗ is regular when N = 7. This improves earlier results of Guo-Wei [20] (N ≤ 4), CowanEsposito-Ghoussoub [2] (N = 5), Cowan-Ghoussoub [4] (N = 6).
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